Chapter 9 Sampling Distributions

If you missed the test on Tuesday, take it Tuesday PM at 3:30 in Mrs. Prestwood's classroom. HW for tonight: Do at least 5 of the 10 problems in REVIEW 3 which follows Chapter 9. Get ready for confidence intervals!!!!

http://www.stat.sc.edu/~west/javahtml/ConfidenceInterval.html


Prepare for the test by working problems from the text and by using a study guide (if you have one) to practice with multiple choice problems. You are welcome to come by in the morning to use a study guide in the classroom.

Your test on Chapter 9 is Tuesday, snow or no snow. Work lots of problems from the chapter. Be sure that you know how to check assumptions or conditions. Do you know when you are calculating probabilities for means and when you are calculating probabilities for proportions? You have to use the right conditions and formulas or you won't be answering the question.

Oh yeah, CiCi's Sunday. Super Bowl Sunday.

For Thursday, 1st and 2nd periods: Complete the questions from the AP exams that we looked at in class. The first one asked for (1) the probability that a measurement of a depth of 2 was negative when the error of the measurement was Normally distributed with mean 0 and std dev 1.5.
(2) What is the probability that at least one of three independent measurements from this distribution was negative?
(3) What is the probability that the average of three independent measurements from this distribution was negative?

Everybody needs to work problem 3 from the 2007 exam.


HW Problems 9.20, .21, 25., .26, &.29 due Wednesday.

HW Problems 9.19, 9.27, 9.30 due Tuesday.
Summary of the three sections of the chapter:
A sampling distribution is the distribution of the sample means of all possible samples of size n. As n (the sample size) increases, the variability of the sample means decreases.
When the underlying (original) distribution is Normally distributed, the sampling distribution for samples of any size n will be Normally distributed.
When the underlying (original) distribution is NOT Normally distributed, the sampling distribution for large sample sizes will be approximately Normally distributed. The closer the original distribution was to Normal, the smaller the sample size required to make the sampling distribution approximately Normally distributed.
These concepts can be applied easily to two cases: measures of x and sample proportions.
For measures of x: The mean of the sampling distribution of x bar is the mean of the underlying distribution of x. The standard deviation of the sampling distribution of x bar is the standard deviation of the underlying distribution /the square root of n.

For sample proportions: When np and nq are both > 10 and n is less than 1/10 of the population, the mean of the p hats is p and the standard deviation of the p hats is the square root of p*q/n AND the distribution of p hats is approximately normal.

< Link to a history of the penny.
Link to a more official history of the penny.

HW Problems 9.32 and 9.34.

I will NOT be available at Open House Thursday night. Please email me with any concerns or join us at CiCi's on Sunday.

HW due Friday, 1/23: 9.10, 9.12, 9.14. Students from per 1 and 2, email your averages to Mrs. L if you did not load them in class. Periods 6 and 7, look up the phrase "planned obsolescence."

This chapter requires you to recall some vocabulary from previous chapters.
HW due Thursday, 1/22: Problems 9.1, .7a-e, .9, .11, .13. You should read through the sections in order to understand the questions.
Also, periods 1 and 2, bring five results from mean(randBin(100,.5,100)).

Measures of central tendency
Median
Mean
Mode


Measures of dispersion (spread)
Range
Standard deviation
Variance
Interquartile range
Absolute deviation

Graphical displays
histogram
line graph
stem and leaf
box and whisker graph
probability density function
scatterplot
cumulative density function
dot plot
pie graph
bar graphs

Pictures speak louder than words

μ = population mean x bar = sample mean (unbiased estimator of mean)

If a sample is drawn at random from a population, the mean of the sample is an excellent estimator of the mean of the population.

σ = population standard deviation s = sample standard deviation

Recall that the calculation of s requires division by n-1 for some complicated reasons.

sx is the standard deviation of the distribution of x
is the standard deviation of the means of the samples of x

E[x] = E[ x bar]

Chapter 8 and the new semester

HW due Thursday: Problems 8.41, 8.43, and 8.44 from the text.

HW due Wednesday: Problems 8.45-8.50. Your test is Tuesday of next week--the day after the Dr. King holiday.

How are these questions similar? How are they different? What strategies would you use to answer each?

1. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 with replacement will not accept text messaging?

2. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 WITHOUT replacement will not accept text messaging?

3. Of the 200,000 cell phones in a metropolitan community, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 WITHOUT replacement will not accept text messaging?

HW due Tuesday, January 13: Probloems 8.19-8.24.

HW due Friday: 8.7, 8.10, 8.11, 8.13, & 8.16.
By Monday, make sure that all of the assigned homework has been done correctly and completely.

HW due Thursday: Problems 1-6 of Chapter 8. Each question requires that you explain how the 4 characteristics is satisfied. Also, define x in each setting. KEY: If your are not counting the number of successes (x) in n trials, it can't possibly be a binomial. If is IS, then check the rest of the conditions.

Yippee! We made to the home stretch.

We will begin Chapter 8 on Wednesday. Tuesday's HW is to complete as much of the crossword puzzle as possible. Some of the answers will become clearer as we progress through binomial and geometric distributions. The plan is to test on Chapter 8 next week and have a chapter test every 2-3 weeks thereafter. This way, we'll be able to dedicate the time after the break to review for the exam.

Let's see. Remove Mirage. Replace batteries. Ask parents to read and sign the syllabus. Bring paper, pencil, and calculator on Wednesday. Be safe.

Did I forget anything? :)